A Semi

The Terpstra and Magel1 multiple comparison test (referred to as the TM test) for umbrella alternative at unknown peak occasionally identifies false concavity in the population means. This work provides a semi-parametric test for umbrella ordering of chances of good health (free from disease) with unknown peak in a 2 × 3 prospective study. The proposed test, a modified version of the TM test, determines true concavity in chances of good health more powerfully and shows low power against false concavity as compared to that of the TM test